已知3sin ²（A+B）／2+cos²（A-B）／2=2,（cosAcosB≠0）求tanAtanB的值?

已知3sin ²（A+B）／2+cos²（A-B）／2=2,（cosAcosB≠0）求tanAtanB的值?
已知3sin ²（A+B）／2+cos²（A-B）／2=2,（cosAcosB≠0）求tanAtanB的值?

已知3sin ²（A+B）／2+cos²（A-B）／2=2,（cosAcosB≠0）求tanAtanB的值?
解3/2(1-cos(A+B))+1/2(1+cos(A-B))=2
3(1-cos(A+B))+(1+cos(A-B))=4
-3cos(A+B)+cos(A-B)=0
-3cosAcosB+3sinAsinB+ cosAcosB+sinAsinB =0
4sinAsinB=2 cosAcosB
tanAtanB=1/2